"open air" mounting a tweeter

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"open air" mounting a tweeter

If a tweeter is supported in free air using as little mounting structure as possible, does it transition at some frequency from 2pi to 4pi radiation depending on the size of the body of the tweeter? That is, if the surface "behind" the radiation of the tweeter has dimensions that are less than equal to the wavelength of the frequency of sound being radiated, does this cause 4pi radiation?

I've designed a speaker system with the tweeter hanging in mid-air and if it radiates 4pi at some point this might not be good for the way that I would like the system to function.

Please let me know what you think and I hope that I am stating the question clearly.
 
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